John works 21 hours a week and earns $157.50. How much does john earn per hour?

Answer:

An equation is basically a way to show a relationship of variables (x,y,a,b, etc) and numbers.

Step-by-step explanation:

Answer:

Shown by explanation.

Step-by-step explanation:

An equation shows a relationship between variables and other factors by defining the variables that are dependent and independent and how these dependent variables are related to the independent variables, this is usually as a result of a prescribed experiment where the relationship of this variables are investigated.

Also remember conditions that favour this experiment must be taken into consideration. And the experiment must always be performed under such conditions.

Answer:

d. no solution

Explanation:

Step 1 - Subtract nine from both sides of the equation

[tex]|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2[/tex]

Step 2 - Remove the absolute value

[tex] |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2[/tex]

Therefore, since positive two is not less than or equal to negative two, there is no solution.

Answer:

The answer is 13

Step-by-step explanation:

Two positive and consecutive old numbers are x and x - 2.

=> x(x - 2) = 143

=> x^2 - 2x - 143 = 0

=> x^2 + 11x - 13x - 143 = 0

=> x(x + 11) - 13(x + 11) = 0

=> (x + 11)(x - 13) = 0

=>  x = -11 (invalid)

or x = 13 (valid), the remaining number is 13 - 2 = 11

=> The two numbers are 11 and 13, and the greater number is 13.

Hope this helps!

:)

Answer:

top: 2

bottom: 13

Step-by-step explanation:

step

by

step

explanation

Answer:

√x+3-13

Step-by-step explanation:

This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.

Answer:

Step-by-step explanation:

all numbers except y = 1

because (f*g)(x) = 1+1/x

and 1/x cannot be equal to 0

Answer:

FALSE

Step-by-step explanation:

The images to solve this problem is in the attachment.

Answer: [tex]F_{fs}[/tex] = 671.0 N; [tex]F_{N}[/tex] = 300 N

Step-by-step explanation: From the image in the attachment and knowing that the box is in equilibrium, i.e., the "sum" of all the forces is 0, it is possible to conclude that:

[tex]F_{fs}[/tex]  = [tex]F_{gx}[/tex] and [tex]F_{N}[/tex] = [tex]F_{gy}[/tex]

Using trigonometry, shown in the second attachment, the values for each force are:

sin 20° = [tex]\frac{F_{gx} }{F_{g} }[/tex]

[tex]F_{gx}[/tex] = [tex]F_{g}[/tex]. sin(20)

[tex]F_{gx}[/tex] = 735.0.913

[tex]F_{gx}[/tex] = 671.0

cos 20° = [tex]\frac{F_{gy} }{F_{g} }[/tex]

[tex]F_{gy}[/tex] = [tex]F_{g}[/tex]. cos (20)

[tex]F_{gy}[/tex] = 735.0.408

[tex]F_{gy}[/tex] = 300

The force of static friction is 671N and normal force is 300N

Answer:

Static force is 251 and the Normal force is 691.

Step-by-step explanation:

Hope this helps!! Have a great day!!    :)

Answer:

3.75 feet

Step-by-step explanation:

The length of the frame is 3 times the width.

Let the width be x.

The length will be 3x.

Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.

The perimeter of a rectangle is:

P = 2(L + W)

=> 10 = 2(3x + x)

=> 10/2 = 4x

5 = 4x

=> x = 5/4 = 1.25 feet

The width is 1.25 feet. The length is therefore:

1.25 * 3 = 3.75 feet

Answer:

t

Step-by-step explanation:

both t and s represent x axis value, t is greater as is on the right side from s  

Answer: t

Step-by-step explanation: khan academy

Steps:

All cans take on the shape of a cylinder, unless you have seen interesting shape of cans like a starfish.

The formula for surface area of a cylinder is

SA = 2πr2 + 2πrh

where:

r = radius

h = height

Since we know the surface area and height, we can plug them in.  Note that we can factor out the 2π.  You will see why we factor out 2π rather than 2πr.

2π(r2 + (20)r) = 396

2π(r2 + 20r) = 396

Divide both sides of the equation by 2π to isolate the r terms.

r2 + 20r = 63.025    

Subtract 63.025 on both sides of the equation.

r2 + 20r - 63.025 = 0

Use the quadratic formula to solve for r:

r = (-b ± √(b2 - 4ac)) / 2a

where:

a = 1

b = 20

c = -63.025

Plug in these values into the formula.  You should get two solutions because of the plus/minus sign.  Accept the positive value of r.

Please mark brainliest

Hope this helps.

Answer:

34°

Step-by-step explanation:

According to the theorem, "any two angles in the same segmant are congruent"

<BED = <BCD

So

<BED = 34°

Answer:

The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).

Critical value t=1.318

Step-by-step explanation:

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=0.165.

The sample size is N=25.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=25-1=24[/tex]

The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.318 \cdot 0.016=0.021[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186[/tex]

The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).

Answer:

The system of inequalities is:

[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]

Step-by-step explanation:

We will write each of the conditions stated in this problem

Patricia wants to buy at least 30 individual songs.

[tex]x\geq30[/tex]

She wants to buy 4 albums at most.

[tex]y\leq4[/tex]

The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.

[tex]10x+1y\leq80[/tex]

The system of inequalities is:

[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]

Answer:

Step-by-step explanation:

Note that 28 + 110 + 42 = 180, and that 28 + 42 + 110 = 180 also.

Since all three angles of one triangle are the same as the corresponding angles of the other triangle, the triangles are similar.

Answer:

y = [tex]y_{1}[/tex] + rise * 2/5

Step-by-step explanation:

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02,   p₂ = 0.07,   p₃ = 0.91

q₁ = 1-p₁ = 0.98 ,   q₂ = 1-p₂ = 0.93 ,   q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

A.

The function will follow multinomial distribution:

[tex]f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})[/tex]

Substitute the values and make a table.

TABLE IN ATTACHMENT

B.

We calculate marginal distribution by:

[tex]P (X=x)=[/tex] ∑ [tex]P(X=x,Y=y)[/tex]

[tex]fx(x)[/tex] can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

[tex]E(X)=[/tex]∑ [tex]xP(X=x)[/tex]

Find E(X):

[tex]E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)[/tex]

[tex]E(X)=0.06[/tex]

Condition probability states:

[tex]P(A|B)=\frac{P(A,B)}{P(B)}[/tex]

It can also be written as:

[tex]f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}[/tex]

Where [tex]f_x(1)\\[/tex] = 0.057624

Calculate the quotient:

[tex]Y|_{x=1}[/tex] = 0 ,  [tex]f_{Y|_X=1[/tex] = 0.862245

[tex]Y|_{x=1}[/tex] = 1 ,  [tex]f_{Y|_X=1[/tex] = 0.132653

[tex]Y|_{x=1}[/tex] = 2 ,  [tex]f_{Y|_X=1[/tex] = 0.000510

[tex]Y|_{x=1}[/tex] = 3 ,  [tex]f_{Y|_X=1[/tex] = 0

Find the dependency:

[tex]f_{XY}(y)=f_X(x)f_Y(y)[/tex]

We found that

[tex]f_{Y|_X=1[/tex] = 0.862245

Calculate [tex]f_Y(1)[/tex] from summing the column from the table

[tex]f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141[/tex]

Which are not equal.

Conclusion:

X and Y are NOT Independent

Answer:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Class width = 12.375

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Step-by-step explanation:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Parameter is a measure that describes the entire population.

Statistic basically describes a sample of the population.

From the given information , the entire 1700 professors at a college is the population and only  35 % own a television is a characteristic, called parameter, of population.

Another objective we are to find here is:

Use the given minimum and maximum data entries, and the number of classes, to find the class width, .

Class width = Maximum - Minimum /No of classes

Given that :

Maximum = 120

Minimum = 21

number of classes = 8

Then;

Class width = 120 - 21 /8

Class width = 12.375

From the given information :

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Answer:

The total price of the shoes including tax is 51.45

Step-by-step explanation:

You could go about this 2 ways.

One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.

The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.

Answer:

The calculated value t = 1.57736 < 1.9845 at 5 % level of significance

Null hypothesis is accepted at 5 % level of significance

There is no significance difference between Design A and Design B

Step-by-step explanation:

Given  sample size of design A

                                            n₁ = 50

sample mean of design A x⁻₁ = 4.1 minutes

Sample standard deviation S₁ = 2.2 minutes

Given  sample size of design B

                                            n₂ = 50

sample mean of design A x⁻₂ = 3.5 minutes

Sample standard deviation S₂ = 1.5 minutes

Null Hypothesis : H₀ : There is no significance difference between Design A and Design B

Alternative Hypothesis : H₁:There is  significance difference between Design A and Design B

Level of significance ∝ = 0.05

Test statistic

[tex]t = \frac{x^{-} _{1}- x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }) } }[/tex]

where

[tex]S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2} S^2_{2} }{n_{1} +n_{2} -2}[/tex]

[tex]S^{2} = \frac{50 (2.2)^{2} +50(1.5)^2}{50+50-2}[/tex]

On calculation , we get

S² = 3.6173

Test statistic

                   [tex]t = \frac{4.1-3.5}{\sqrt{3.617(\frac{1}{50} +\frac{1}{50} }) }[/tex]

On calculation , we get

   t = 1.57736

Degrees of freedom

ν = n₁ + n₂ -2 = 50 +50 -2 =98

t₀.₀₂₅ ,₉₈ = 1.9845

The calculated value t = 1.57736 < 1.9845 at 5 % level of significance

null hypothesis is accepted

Answer:

   9 in

Step-by-step explanation:

For an n-sided polygon, the length of the apothem is ...

  a = r·cos(180°/n)

We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...

  a = (10 in)cos(30°) ≈ 8.66 in

Rounded to the nearest inch, the apothem is 9 in.

Answer:

Step-by-step explanation:

The test to use is the t-test of independent means.

To determine the cutoff for the study then you need to find the degree of freedom and the alpha level. After the hypothesis testing, the calculated t value is then compared to the critical t value from the t distribution table using the degrees of freedom.

Answer:

an example of a literal question is "what size do you wear", "what time does the show start", "who was the protagonist in your story"  etc

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mean = (87 + 105 + 130 + 160 + 180 + 195 + 135 + 145 + 213 + 105 + 145 + 151 152 + 136 + 87 + 99 + 92 + 119 + 129)/19 = 129

Variance = (summation(x - mean)²/n

Standard deviation = √(summation(x - mean)²/n

n = 19

Variance = [(87 - 129)^2 + (105 - 129)^2 + (130 - 129)^2+ (160 - 129)^2 + (180 - 129)^2 + (195 - 129)^2 + (135 - 129)^2 + (145 - 129)^2 + (213 - 129)^2 + (105 - 129)^2 + (145 - 129)^2 + (151 - 129)^2 + (152 - 129)^2 + (136 - 129)^2 + (87 - 129)^2 + (99 - 129)^2 + (92 - 129)^2 + (119 - 129)^2 + (129 - 129)^2]/19 = 23634/19 1243.895 min

Standard deviation = √1243.895 = 35.269 min

60 minutes = 1 hour

Converting the variance to hours,

Each division would have been divided by 60². 60² can be factorized out

Variance = 23634/60² = 6.565 hours

Converting the standard deviation to hours, it becomes

√6.565 = 2.562 hours

Answer:

7/24

Step-by-step explanation:

Tangent is opposite over adjacent. You know that the opposite leg is 14 but you don't know the adjacent.

To find the unknown leg, use Pythagorean theorem so that 50^2-14^2= leg. The length is 48.

14/48= tan B

7/24= tan B

Answer:

The distribution pattern that will have variance greater than mean is one where the population of species is clustered and thus far from the mean abundance of species per unit area.

This distribution pattern can be found, using the POISSON distribution.

Step-by-step explanation:

Variance is a measure of dispersion while Mean is a measure of central tendency.

The mean is the average of all values (in this case, the abundance or concentration of species per unit area). It is the sum total of all values, divided by the number of values there are.

The variance of a given set of data, on the other hand, is a measure of the spread or distance or dispersal of the data from the mean. It measures the spread between each datum/value and the mean value.

The relationship between mean and variance surely reflects the pattern that the distribution will take. The kind of distribution pattern that will have a greater variance than mean is a Poisson distribution. Sample size is usually large here. Since the variance is greater than the mean, the population is a clustered or clumped distribution.

Answer:

89 degrees

Step-by-step explanation:

The angle 1 is the same as angle 3.

Angle 2 is the same as angle 4.

The sum of these four angles is 360 degrees.

We have that:

Angle 2 = Angle 4 = 7x - 14

Angle 3 = Angle 1 = 5x + 14

Finding x:

Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360

2*(5x + 14) + 2*(7x - 14) = 360

10x + 28 + 14x - 28 = 360

24x = 360

x = 15

Angle 1:

5x + 14 = 5*15 + 14 = 89 degrees

Answer:

I think it is B

Step-by-step explanation:

Answer:

Probabilty= 4.171. *10^-4

Step-by-step explanation:

bridge is made up of 13 cards

probability that a bridge chosen at random contains

6 of one suit, 4 of another, and 3 of another

Probabilty of 6 = 13C6

Probabilty of 4 = 13C4

Probabilty of 3 = 13C3

Then total= 53C13

Probabilty =( 13C6*13C4*13C3)/53C13

Probabilty=( 1716*715*286)/53C13

Probabilty= 4.171. *10^-4

Answer:

The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances. For example, |x| + 3 = |x + 3| only when x ≥ 0. ... The composition of one-to-one functions is always one-to-one.

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Answer:

35

Step-by-step explanation:

3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9

a+b=?

------

all numbers get cancelled apart from the first denominator and the last numerator:

1/2*a= 9

then

a+b= 18+17= 35